Editing Array processing (section)

=== Spatial whitening ===
This scheme attempts to make the interference-plus-noise term spectrally white. To do this, left and right multiply <math>\mathbf{R}</math> with inverse square root factors of the interference-plus-noise terms.

<math>\tilde{\mathbf{R}} = (\sigma_s^2 \mathbf{a} \mathbf{a}^{\dagger} + \sigma_n^2 \mathbf{I})^{-{\frac{1}{2}}} \mathbf{R}(\sigma_s^2 \mathbf{a} \mathbf{a}^{\dagger} + \sigma_n^2 \mathbf{I})^{-{\frac{1}{2}}}</math>

The calculation requires rigorous matrix manipulations, but results in an expression of the form:

<math>\tilde{\mathbf{R}} = (\cdot)^{-{\frac{1}{2}}} \mathbf{R}_v(\cdot)^{-{\frac{1}{2}}} + \mathbf{I}</math>

This approach requires much more computationally intensive matrix manipulations, and again the visibilities covariance matrix is altered.<ref>{{cite journal
 |author1=Amir Leshem |author2=Alle-Jan van der Veen | date = August 16, 2000
 | title = Radio astronomical imaging in the presence of strong radio interference
 | journal = IEEE Transactions on Information Theory
 | volume = 46
 | issue = 5
 | pages = 1730–1747
 | doi = 10.1109/18.857787
 |arxiv = astro-ph/0008239|s2cid=4671806 }}</ref>